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In this thesis, we present our updated determinations for the leading order and higher order hadronic vacuum polarisation contributions to the anomalous magnetic moment of the muon (a_{\mu} {had,LOVP}, a_{\mu} {had,HOVP}), and for the hadronic contributions to the running of the QED coupling at the Z-boson mass (\Delta\alpha_{had} {(5)}(M_Z 2)). At present the Standard Model (SM) predictions of the anomalous magnetic moment of the muon a_{\mu} {SM} is lower than the experimental measurement a_{\mu} {exp}$ by about 3 standard deviations. The precision of a_{\mu} {SM} is limited by hadronic contributions, of which a_{\mu} {had,LOVP} has the largest uncertainty. Therefore improving the accuracy and precision of a_{\mu} {had,LOVP} will help to clarify the origin of the discrepancy between theory and experiment. The running of the QED coupling at the Z-boson mass \alpha(M_Z 2) is the least precise of the three parameters that is usually taken to define the electroweak sector of the SM. Its precision is limited by \Delta\alpha_{had} {(5)}(M_Z 2), and is a significant limiting factor for precision electroweak physics, e.g. the indirect determination of Higgs boson mass. We describe in detail our refined data-driven approach, which processes and combines a large number of e +e - hadronic annihilation data for use in our determinations. Error treatment is of course, also discussed in depth. We present a detailed breakdown of all the contributions to a_{\mu} {had,LOVP}, including the many new, more precise data used along with discussions on their impacts. We also perform an improved sum rule analysis for a specific energy region, which assists us in discriminating between two different choices of using data. Comparisons with previous analyses as well as with another group's recent determination are also made. For \Delta\alpha_{had} {(5)}(M_Z 2), we summarise the main results, discussing their effects as well as the comparison with other groups. More focus is given to a separate procedure used for preparing a set of new data that will improve the description of \alpha(q 2). We conclude the thesis by summing our a_{\mu} {had,LOVP}, a_{\mu} {had,HOVP} results with the latest predictions of contributions from the other sectors of the SM, leading to our own value for a_{\mu} {SM}. This is then discussed and compared to other recent determinations. Results for \Delta\alpha_{had} {(5)}(M_Z 2) and \alpha(M_Z 2) are also briefly reviewed. Finally, a summary of the whole thesis and future prospects in this area of study are given.

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Quantum electrodynamic theory (QED) in the vicinity of macroscopic structures has achieved new importance due to its applicability, particularly in nanotechnology. There are many powerful methods for studying QED near media with diverse properties and geometries. However, applying them to a particular problem generally necessitates extensive numerical calculations. This is not the case for simple systems of high symmetry, in which the electromagnetic field can be quantised by explicit mode expansion, allowing exact analytic calculations. In the present thesis, we calculate the energy-level shift of a ground state atom near a non-dispersive and non-dissipative dielectric slab. The shift is due to the interaction of the atom with electromagnetic field fluctuations, which in turn are affected by the presence of the slab. Thus, a quantisation of the electromagnetic field in the presence of a layered system is required. We derive the field modes, which comprise of a continuous set of travelling modes (with incident, reflected and transmitted parts) and trapped modes, subject to repeated total internal reflection and emerge as an evanescent field outside the slab, they only exist at certain discrete frequencies. The shift is obtained by means of second-order perturbation theory. It splits up naturally into two contributions, due to the different nature of the modes, and a problem arises when we have to add them all. We have come up with a convenient method of summing over all modes, and its validity has been demonstrated by proving the completeness. The calculation of the shift follows as an application of our method. The result is analysed asymptotically for various regions, reducing to simple formulas that can be utilised in recent experiments, in which the thickness of the substrate matters.

Ce travail vise à contribuer à l’amélioration de notre connaissance de l’électrodynamique quantique des états liés, par des mesures de haute précision dans des états exotiques de la matière. Bien que notre connaissance de l’électrodynamique quantique des états liés et du problème relativiste à plusieurs corps aient fait des progrès importants ces dernières années, il reste des questions fondamentales dont la résolution nécessite d’augmenter le nombre et la précision des tests expérimentaux. La première partie de ce travail a été réalisée dans le cadre de l’expérience récente sur les ions muoniques d’hélium (μ4He+ et μ3He+) conduite par la collaboration CREMA. Cette expérience vise à fournir de nouvelles valeurs précises pour les rayons de charge moyens des noyaux des isotopes stables de l’hélium. Ces valeurs sont extraites de la mesure du déplacement de Lamb, c’est-à-dire, de la mesure de la différence d’énergie entre les États 2S − 2P. Une mesure des énergies de transition d’une précision d’au moins 50 ppm, permet de déterminer les rayons de charge des noyaux des isotopes d’hélium avec une incertitude de 0,03%, dix fois plus précise que les résultats précédents obtenus à partir de la diffusion d’électrons. La deuxième partie de ce travail a été de réaliser des mesures de haute précision de transitions de rayons X dans des ions fortement chargés, à l’aide d’un spectromètre à double cristal plan. Ces ions étaient produits dans le plasma d’une source d’ions de type ECRIS (electron-cyclotron resonance ion source). Le spectromètre utilisé est non seulement capable de fournir des mesures de haute précision, mais aussi des mesures sans référence à des énergies de transition théorique ou expérimentales. Quatre énergies de transition de n = 2 → n = 1 ont été mesurées pour des ions d’argon de trois états de charge différents, héliumoïde, lithiumoïde et berylliumoïde, avec une précision meilleure que 3 ppm. La largeur naturelle de chaque raie a également été obtenue expérimentalement. Les résultats trouvés sont en excellent accord avec les calculs théoriques les plus récents. / This work aims to provide insight on Bound-State Quantum-Electrodynamics (BSQED) by experimental fundamentals high-precision tests in exotic states of matter. Although BSQED and the relativistic many-body problem have been undergoing important progress, there are still some issues that require the increase of the number and accuracy of experimental fundamental tests. The first part of this work was done within the framework of the recent experiment in muonic helium ions (μ4He+ and μ3He+) by the CREMA collaboration. This experiment, aims to provide new accurate values for the root-mean-square (rms) charge radii of the helium isotopes nuclei that are extracted from the measurement of the Lamb Shift, i.e., the measurement of the energy difference between the 2S − 2P states. With the goal of measuring the transition energies with an accuracy of at least 50 ppm, the rms charge radii of the helium isotopes will be determined with an uncertainty of 0.03%, a factor of ten more precise than previous results obtained from electron scattering. The second part of this work aims the high-precision measurement of x-ray transitions in Highly-Charged Ions (HCI) using a Double-Crystal Spectrometer (DCS). These ions were produced in the plasma of an Electron-Cyclotron Resonance Ion Source (ECRIS). This kind of spectrometer is able not only to provide high-precision measurements but also reference-free measurements, without reference to any theoretical or experimental energy. Four transitions energies from n = 2 → n = 1 have been measured in an argon plasma in three different charge states, He-, Be- and Li-like, with an accuracy of better than 3 ppm. Besides the energies, the natural width of each transition has also been experimentally obtained. The obtained results are in excellent agreement with the most recent theoretical calculations.

Dans cette thèse, nous étudions des circuits de boîtes quantiques à base de nanotubes de carbone intégrés dans une cavité micro-onde. Cette architecture générale permet de sonder le circuit en utilisant simultanément des mesures de transport et des techniques propre au domaine de l’Electrodynamique quantique sur circuit. Les deux expériences réalisées durant cette thèse exploitent la capacité des métaux de contact à induire des corrélations de spins dans les boites quantiques. La première expérience est l’étude d’une lame s´séparatrice à paires de Cooper, initialement imaginée comme une source d’électrons intriqués. Le couplage du circuit aux photons dans la cavité permet de sonder la dynamique interne du circuit, et a permis d’observer des transitions de charge habillées par le processus de séparation des paires de Cooper. Le couplage fort entre une transition de charge dans un circuit de boîtes quantiques et des photons en cavité, a été observée pour la première fois dans ce circuit. Une nouvelle technique de fabrication a aussi été développé pour intégrer un nanotube de carbone cristallin au sein du circuit de boîtes quantiques. La pureté et l’accordabilité de cette nouvelle génération de circuit a rendu possible la seconde expérience. Cette dernière utilise deux vannes de spins non colinéaire afin de produire une interface cohérente entre le spin d’un électron dans une double boite quantique, et un photon dans une cavité. Des transitions de spins très cohérentes ont été observée, et nous donnons un modèle sur l’origine de la décohérence du spin comprenant le bruit en charge et les fluctuations des spins nucléaires. / In this thesis, we study carbon nanotubes based quantum dot circuits embedded in a microwave cavity. This general architecture allows one to simultaneously probe the circuit via quantum transport measurements and using circuit quantum electrodynamics techniques. The two experiments realized in this thesis use metallic contacts of the circuit as a resource to engineer a spin sensitive spectrum in the quantum dots. The first one is a Cooper pair splitter which was originally proposed as a source of non local entangled electrons. By using cavity photons as a probe of the circuit internal dynamics, we observed a charge transition dressed by coherent Cooper pair splitting. Strong charge-photon coupling in a quantum dot circuit was demonstrated for the first time in such a circuit. A new fabrication technique has also been developed to integrate pristine carbon nanotubes inside quantum dot circuits. The purity and tunability of this new generation of devices has made possible the realization of the second experiment. In the latter, we uses two non-collinear spin-valves to create a coherent interface between an electronic spin in a double quantum dot and a photon in a cavity. Highly coherent spin transitions have been observed. We provide a model for the decoherence based on charge noise and nuclear spin fluctuations.